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<h3 class="heading"><span class="type">Paragraph</span></h3>
<p><dfn class="terminology">Solution</dfn> The characteristic equation is</p>
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\begin{equation*}
4 r^2+12 r+9=0~\to~(2 r+3)^2=0~\to~r_1=-\frac{3}{2}=r_2.
\end{equation*}
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<p class="continuation">Thus one solution is</p>
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\begin{equation*}
y_1=e^{-\frac{3}{2} x}.
\end{equation*}
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<p class="continuation">The second solution is</p>
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\begin{equation*}
y_2=x y_1=x e^{-\frac{3}{2}x} .
\end{equation*}
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<p class="continuation">The general solution is</p>
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\begin{equation*}
y=C_1 e^{-\frac{3}{2} x}+C_2 x e^{-\frac{3}{2} x}.
\end{equation*}
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<span class="incontext"><a href="sec3_5.html#p-106" class="internal">in-context</a></span>
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